Problem: What do the following two equations represent? $-3x-2y = 4$ $8x-12y = -3$
Answer: Putting the first equation in $y = mx + b$ form gives: $-3x-2y = 4$ $-2y = 3x+4$ $y = -\dfrac{3}{2}x - 2$ Putting the second equation in $y = mx + b$ form gives: $8x-12y = -3$ $-12y = -8x-3$ $y = \dfrac{2}{3}x + \dfrac{1}{4}$ The slopes are negative inverses of each other, so the lines are perpendicular.